In Exercises 21-24, we return to Exercises 1-4 in Section 2.3 . (For convenience, the equations are reproduced below.) For each second-order equation,
(a) convert the equation to a first-order, linear system;
(b) compute the eigenvalues and eigenvectors of the system;
(c) for each eigenvalue, pick an associated eigenvector
(d) compare the results of your calculations in part (c) with the results that you obtained when you used the guess-and-test method of Section 2.3
22.
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Differential Equations
- Please explain how to reach the answer. Consider a system with complex eigenvalues. The system's general solution is given below. Show if there are any straight line solutions and draw them. Also draw nullclines and determine the system's behavior...arrow_forwardFind the eigen values of the given system of linear equationsarrow_forwardPlease answer only the second question (question 2) correctly and with as much detail/explanation as possible. Please make sure you have the correct answer. Thank you! You must find the eigenvalues and eigenvectors of each coefficient matrix and use these to find the general solution of the system.arrow_forward
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- Match pairs of eigenvalues to the phase portraits of two dimensional systems. A₁-1, A₂=-2 A₁-2+ 3i, A₂ = -2-3i A₁ = 5, Ag= -3 A₁ = 1, A₂= 2 A₁=1+i√5, ₂-1-i√5 A₁21, A₂=-2i a. b.arrow_forward(a) convert the equation to a first-order, linear system; (b) compute the eigenvalues and eigenvectors of the system; (e) for each eigenvalue, pick an associated eigenvector V, and determine the solution Y() to the system; and (d) compare the results of your calculations in part (c) with the results that you ob- tained when you used the guess-and-test method of Section 2.3. d²y d12 dy +5+6y=0 dtarrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,